can You calculate the blue Area

[@STEAMerBear]

Okay, before we start I see the three squares that total 40cm in length, making the right triangle of 20cm by 40cm. The 8cm square includes a shaded similar triangle of 4cm by 8cm and area 16cm^2. The 12 cm square has a shaded trapezoid of height 12cm with bases of 8cm and 2cm having an area of 60cm^2. Finally the 20cm square has a 10cm by 20 cm shaded triangle with area 100cm^2. For a total of 176cm^2. Let’s see how I did…

[@MathandEngineering]

Okay so you mean, you solved it without even a pen and a paper, like you did all the solving in you mind, wow that's really amazing. As it is, experience is the best teacher

[@STEAMerBear]

@@MathandEngineering yes! I try to emphasize mental math in my classroom largely because American students are so very technology dependent, with many lacking much number sense at all. I have been using Prof. Arthur Benjamin’s methods, detailed in his book “No Calculator? No Problem! Mastering Mental Math”

[@MathandEngineering]

Good day sa, i wanna ask for your opinion, a friend asked me to prove from a triangle ABC that sin(A/2) ≤ a/b + c Which I understand to be sin(A/2) = a/b + c. Or Sin(A/2) < a/b + c So I found it impossible that sin(A/2) = a/b + c Because the sine ratio of any angle can never be equal or greater than 1, it is always less than 1, But in a triangle A B C, no matter what it's length are, a/b + c is always going to be greater than 1. I told them that it was impossible but he insisted that it was possible, That's why I am asking for you opinion, am I missing something?

[@STEAMerBear]

@@MathandEngineering I need to take some time working on this before I answer.

[@MathandEngineering]

Ok thanks sir, I'll be waiting for your answer,